# Math Help - Factoring

1. ## Factoring

Can someone show me why

(a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)

2. Use the difference of two squares pattern:
$x^2 - y^2 = (x - y)(x + y)$

Substitute "a - b" for x and "c + d" for y:
\begin{aligned}
(a - b)^2 - (c + d)^2 &= [(a - b) - (c + d)][(a - b) + (c + d)] \\
&= (a - b - c - d)(a - b + c + d)
\end{aligned}

3. Originally Posted by Alan306090
Can someone show me why

(a - b) ^2 - (c + d)^2 = (a-b-c-d)(a-b+c+d)
let $(a-b) = x$ and $(c+d) = y$

working from the right side ...

$(a-b-c-d)(a-b+c+d) =$

$[(a-b)-(c+d)][(a-b)+(c+d)] =$

$[x-y][x+y] =$

$x^2-y^2 =$

$(a-b)^2 - (c+d)^2$